test/aoj/CGL_3_C.test.cpp

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Last update: 2024-01-08 01:08:59+09:00
Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C

Depends on

Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C"

#include "../../geometry/geometry.hpp"
#include "../../geometry/intersect.hpp"

#include <bits/stdc++.h>
using namespace std;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    int n;
    cin >> n;
    vector<Vec> pts(n);
    for (auto& x : pts) cin >> x;
    int q;
    cin >> q;
    while (q--) {
        Vec p;
        cin >> p;
        cout << intersect(pts, p) << "\n";
    }
}

#line 1 "test/aoj/CGL_3_C.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_C"

#line 2 "geometry/geometry.hpp"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <complex>
#include <iostream>
#include <numbers>
#include <numeric>
#include <vector>

// note that if T is of an integer type, std::abs does not work
using T = double;
using Vec = std::complex<T>;

std::istream& operator>>(std::istream& is, Vec& p) {
    T x, y;
    is >> x >> y;
    p = {x, y};
    return is;
}

T dot(const Vec& a, const Vec& b) { return (std::conj(a) * b).real(); }

T cross(const Vec& a, const Vec& b) { return (std::conj(a) * b).imag(); }

constexpr T PI = std::numbers::pi_v<T>;
constexpr T eps = 1e-10;
inline bool eq(T a, T b) { return std::abs(a - b) <= eps; }
inline bool eq(Vec a, Vec b) { return std::abs(a - b) <= eps; }
inline bool lt(T a, T b) { return a < b - eps; }
inline bool leq(T a, T b) { return a <= b + eps; }

struct Line {
    Vec p1, p2;
    Line() = default;
    Line(const Vec& p1, const Vec& p2) : p1(p1), p2(p2) {}
    Vec dir() const { return p2 - p1; }
};

struct Segment : Line {
    using Line::Line;
};

struct Circle {
    Vec c;
    T r;
    Circle() = default;
    Circle(const Vec& c, T r) : c(c), r(r) {}
};

using Polygon = std::vector<Vec>;

Vec rot(const Vec& a, T ang) { return a * Vec(std::cos(ang), std::sin(ang)); }

Vec perp(const Vec& a) { return Vec(-a.imag(), a.real()); }

Vec projection(const Line& l, const Vec& p) {
    return l.p1 + dot(p - l.p1, l.dir()) * l.dir() / std::norm(l.dir());
}

Vec reflection(const Line& l, const Vec& p) {
    return T(2) * projection(l, p) - p;
}

// 0: collinear
// 1: counter-clockwise
// -1: clockwise
int ccw(const Vec& a, const Vec& b, const Vec& c) {
    if (eq(cross(b - a, c - a), 0)) return 0;
    if (lt(cross(b - a, c - a), 0)) return -1;
    return 1;
}

void sort_by_arg(std::vector<Vec>& pts) {
    std::ranges::sort(pts, [&](auto& p, auto& q) {
        if ((p.imag() < 0) != (q.imag() < 0)) return (p.imag() < 0);
        if (cross(p, q) == 0) {
            if (p == Vec(0, 0))
                return !(q.imag() < 0 || (q.imag() == 0 && q.real() > 0));
            if (q == Vec(0, 0))
                return (p.imag() < 0 || (p.imag() == 0 && p.real() > 0));
            return (p.real() > q.real());
        }
        return (cross(p, q) > 0);
    });
}
#line 3 "geometry/intersect.hpp"

bool intersect(const Segment& s, const Vec& p) {
    Vec u = s.p1 - p, v = s.p2 - p;
    return eq(cross(u, v), 0) && leq(dot(u, v), 0);
}

// 0: outside
// 1: on the border
// 2: inside
int intersect(const Polygon& poly, const Vec& p) {
    const int n = poly.size();
    bool in = 0;
    for (int i = 0; i < n; ++i) {
        auto a = poly[i] - p, b = poly[(i + 1) % n] - p;
        if (eq(cross(a, b), 0) && (lt(dot(a, b), 0) || eq(dot(a, b), 0)))
            return 1;
        if (a.imag() > b.imag()) std::swap(a, b);
        if (leq(a.imag(), 0) && lt(0, b.imag()) && lt(cross(a, b), 0)) in ^= 1;
    }
    return in ? 2 : 0;
}

int intersect(const Segment& s, const Segment& t) {
    auto a = s.p1, b = s.p2;
    auto c = t.p1, d = t.p2;
    if (ccw(a, b, c) != ccw(a, b, d) && ccw(c, d, a) != ccw(c, d, b)) return 2;
    if (intersect(s, c) || intersect(s, d) || intersect(t, a) ||
        intersect(t, b))
        return 1;
    return 0;
}

// true if they have positive area in common or touch on the border
bool intersect(const Polygon& poly1, const Polygon& poly2) {
    const int n = poly1.size();
    const int m = poly2.size();
    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < m; ++j) {
            if (intersect(Segment(poly1[i], poly1[(i + 1) % n]),
                          Segment(poly2[j], poly2[(j + 1) % m]))) {
                return true;
            }
        }
    }
    return intersect(poly1, poly2[0]) || intersect(poly2, poly1[0]);
}

// 0: inside
// 1: inscribe
// 2: intersect
// 3: circumscribe
// 4: outside
int intersect(const Circle& c1, const Circle& c2) {
    T d = std::abs(c1.c - c2.c);
    if (lt(d, std::abs(c2.r - c1.r))) return 0;
    if (eq(d, std::abs(c2.r - c1.r))) return 1;
    if (eq(c1.r + c2.r, d)) return 3;
    if (lt(c1.r + c2.r, d)) return 4;
    return 2;
}
#line 5 "test/aoj/CGL_3_C.test.cpp"

#include <bits/stdc++.h>
using namespace std;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    int n;
    cin >> n;
    vector<Vec> pts(n);
    for (auto& x : pts) cin >> x;
    int q;
    cin >> q;
    while (q--) {
        Vec p;
        cin >> p;
        cout << intersect(pts, p) << "\n";
    }
}